An explicit form for Kerov's character polynomials

Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that this polynomial has integer coefficients, and made various conjectures. Recently, Sniady has proved Biane's conjectured explicit form for the first family of nontrivial terms in this polynomial. In this paper, we give an explicit expression for all terms in Kerov's character polynomials. Our method is through Lagrange inversion.Comment: 17 pages, 1 figur

Proof of Stanley's conjecture about irreducible character values of the symmetric group

R. Stanley has found a nice combinatorial formula for characters of irreducible representations of the symmetric group of rectangular shape. Then, he has given a conjectural generalisation for any shape. Here, we will prove this formula using shifted Schur functions and Jucys-Murphy elements.Comment: 9 page

Whites' perceptions of biracial individuals' race shift when biracials speak out against bias

Previous research suggests that a person’s racial identity shapes the way others respond when that person speaks out against racial prejudice. In the present research, we consider instead how speaking out against racial prejudice shapes people’s impressions of a confronter’s racial identity, such as experiences with discrimination, stereotype enactment, and even phenotype. Two experiments found that White perceivers evaluated a Black/White biracial person who spoke out against (versus remained silent to) racial prejudice as more stigmatized and Black-identified, and as having more stereotypically Black (vs. White) preferences and Black (vs. White) ancestry when they confronted. The faces of biracial confronters (vs. non-confronters) were also recalled as more phenotypically Black (vs. White; Study 2). This evidence suggests that speaking out against bias colors Whites’ impressions of a biracial target across both subjective and objective measures of racial identity. Implications for interracial interactions and interpersonal perception are discussed

Respiratory metabolism in Oreochromis mossambicus, Peters under different environmental conditions

Oxygen consumption in Oreochromis mossambicus, Peters (3-60g in weight) was measured under different stress conditions at a constant temperature of 20±1°C. The rate of oxygen consumption was significantly higher (0.170 ml gˉ¹hˉ¹)at a salinity of 30x10ˉ³ compared with that (0.132ml gˉ¹hˉ¹) in freshwater. The oxygen consumption was also found to be affected by changes in pH. Weight specific rate decreased significantly from 0.113 to 0.045 ml gˉ¹hˉ¹ with increasing body weight. A positive correlation was recorded between availability of dissolved oxygen and the rate of oxygen consumption by the fish. While copper sulphate and malachite green inhibited the respiratory metabolism, formaldehyde treatment raised it from 0.088 to 0.118ml gˉ¹hˉ¹

Is education a fundamental right? People's lay theories about intellectual potential drive their positions on education

Does every child have a fundamental right to receive a high quality education? We propose that people’s beliefs about whether “nearly everyone” or “only some people” have high intellectual potential drive their positions on education. Three studies found that the more people believed that nearly everyone has high potential, the more they viewed education as a fundamental human right. Further, people who viewed education as a fundamental right, in turn, (1) were more likely to support the institution of free public education; (2) were more concerned upon learning that students in the country were not performing well academically compared to students in peer nations; and (3) were more likely to support redistributing educational funds more equitably across wealthier and poorer school districts. The studies show that people’s beliefs about intellectual potential can influence their positions on education, which can affect the future quality of life for countless students

What happens after prejudice is confronted in the workplace? How mindsets affect minorities' and women's outlook on future social relations

Organizations are increasingly concerned with fostering successful diversity. Toward this end, diversity research has focused on trying to reduce prejudice and biased behavior. But what happens when prejudice in the workplace inevitably occurs? Research also needs to focus on whether recovery and repair of social relations after incidents of prejudice are possible. To begin investigating this question, we develop a new framework for understanding reactions to prejudice in the workplace. We hypothesized that when women and minorities choose to confront a prejudiced comment in a workplace interaction (vs. remain silent) and hold a growth (vs. fixed) mindset — the belief that others can change — they remain more positive in their subsequent outlook in the workplace. Studies 1a, 1b, and 2 used hypothetical workplace scenarios to expose participants to someone who expressed bias; Study 3 ensured real-world relevance by eliciting retrospective accounts of workplace bias from African American employees. Across studies, women and minorities who confronted the perpetrator of prejudice exhibited more positive subsequent expectations of that co-worker when they held a growth mindset. Importantly, these more positive expectations were associated with reports of greater workplace belonging (Study 2), ratings of improved relations with co-workers who had displayed bias (Study 3), and greater workplace satisfaction (Studies 2-3). Thus, a growth mindset contributes to successful workplace diversity by protecting women’s and minorities’ outlook when they opt to confront expressions of bias

Identical applicant but different outcomes: the impact of gender versus race salience in hiring

People belong to multiple social groups, which may have conflicting stereotypic associations. A manager evaluating an Asian woman for a computer programming job could be influenced by negative gender stereotypes or by positive racial stereotypes. We hypothesized that evaluations of job candidates can depend upon what social group is more salient, even when both are apparent. In three studies, using student (Study 1) and non-student (Studies 2 and 3) samples, we compared ratings of an Asian-American female applicant, after subtly making her race or gender salient in stereotypically male employment contexts. Consistent with our predictions, we found evidence that men rated her as more skilled (Studies 1 and 3), more hirable (Studies 1-3), and offered her more pay (Study 2) in science and technology-related positions when her race, rather than gender, was salient. The theoretical implications for person perception and practical implications in employment contexts are discussed

Fuzzy Logic Controller Stability Analysis Using a Satisfiability Modulo Theories Approach

While many widely accepted methods and techniques exist for validation and verification of traditional controllers, at this time no solutions have been accepted for Fuzzy Logic Controllers (FLCs). Due to the highly nonlinear nature of such systems, and the fact that developing a valid FLC does not require a mathematical model of the system, it is quite difficult to use conventional techniques to prove controller stability. Since safety-critical systems must be tested and verified to work as expected for all possible circumstances, the fact that FLC controllers cannot be tested to achieve such requirements poses limitations on the applications for such technology. Therefore, alternative methods for verification and validation of FLCs needs to be explored. In this study, a novel approach using formal verification methods to ensure the stability of a FLC is proposed. Main research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a nonlinear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but inconclusive for Lyapunov stability

Use of a Subcutaneous Insulin Computerized GlucoStabilizer™ Program on Glycemic Control in the Intensive Care Setting: A Retrospective Data Analysis.

Background: Despite guidelines that recommend strongly against Sliding Scale Insulin (SSI) it continues to be the most commonly insulin regimen used in hospitals to treat hyperglycemia. In addition to being reactionary to a glucose that has already increased, SSI offers practical challenges in the randomness of the doses of insulin prescribed and often a disconnect with glucose testing that should be occurring in congruence to the insulin dosing. While many clinical trials have shown improved glycemic control in critical care patients receiving intravenous insulin; few studies have demonstrated the efficacy of subcutaneous (SQ) insulin in this setting. In this study, we have evaluated the safety and efficacy of SQ insulin administration utilizing a computerized program, the Clarian GlucoStabilizer™ Subcutaneous Program (CGS-SQ) in the intensive care unit (ICU). This program is designed to overcome some of the most common barriers of SQ insulin delivery, those of dose calculation and timing. Methods: A computerized SQ insulin delivery program -The Clarian GlucoStabilizer™ Subcutaneous Program (CGS-SQ)- was made available to ICU practitioners, facilitating standardized calculation of insulin doses and incorporating reminder alarms for blood glucose (BG) testing. This program used three defaults Insulin Sensitivity Factors (ISF) and Insulin to Carbohydrate Ratios (CR) to calculate insulin doses. Additionally, there is an option for practitioner determined ISF and ICR. Patients, aged ≥ 18 years, initiated on the CGS-SQ and admitted to the (ICU) were eligible for inclusion in this retrospective evaluation. Patients were divided into four groups based on initial insulin sensitivity factor (ISF) and carbohydrate ratio (CR). Three of the groups used a default ISF and CR; ISF 60, CR 15; ISF 30, CR 10 and ISF 15, CR 8. These groups were compared with those where the practitioner specified an individualized ISF and CR, referred to as PDS (practitioner defined setting). Primary endpoints included: mean glucose, time to target glucose, hyperglycemic and hypoglycemic events. Results: In the 1,384 patients identified, patients initiated with a predefined setting had lower mean glucose compared to patients with PDS (ISF 60, CR 15: 135 mg/dL vs. ISF 30, CR 10: 140 mg/dL vs. ISF 15, CR 8: 134 mg/dL vs. PDS: 143 mg/dL; p \u3c 0.0001). Patients in the default settings had shorter time to target glucose and decreased incidence of hyperglycemia and hypoglycemia. Conclusions: Using a system of computerized prompts with standardization of insulin dose calculation, SQ insulin can be effectively used in the treatment of ICU patients to target BG of 100-150 mg/dL with minimal risk of hypoglycemia